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On singular boundary points of complex functions
Published online by Cambridge University Press: 26 February 2010
Abstract
Let f be a complex valued function from the open upper halfplane E of the complex plane. We study the set of all z∈∂E such that there exist two Stoltz angles V1, V2 in E with vertices in z (i.e., Vi is a closed angle with vertex at z and Vi\{z} ⊂ E, i = 1, 2) such that the function f has different cluster sets with respect to these angles at z. E. P. Dolzhenko showed that this set of singular points is G∂σ and σ-porous for every f. He posed the question of whether each G∂σ σ-porous set is a set of such singular points for some f. We answer this question negatively. Namely, we construct a G∂ porous set, which is a set of such singular points for no function f.
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- Research Article
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- Copyright © University College London 1998
References
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